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Theorem jaoded 39307
 Description: Deduction form of jao 945. Disjunction of antecedents. (Contributed by Alan Sare, 3-Dec-2015.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
jaoded.1 (𝜑 → (𝜓𝜒))
jaoded.2 (𝜃 → (𝜏𝜒))
jaoded.3 (𝜂 → (𝜓𝜏))
Assertion
Ref Expression
jaoded ((𝜑𝜃𝜂) → 𝜒)

Proof of Theorem jaoded
StepHypRef Expression
1 jaoded.1 . 2 (𝜑 → (𝜓𝜒))
2 jaoded.2 . 2 (𝜃 → (𝜏𝜒))
3 jaoded.3 . 2 (𝜂 → (𝜓𝜏))
4 jao 945 . . 3 ((𝜓𝜒) → ((𝜏𝜒) → ((𝜓𝜏) → 𝜒)))
543imp 1101 . 2 (((𝜓𝜒) ∧ (𝜏𝜒) ∧ (𝜓𝜏)) → 𝜒)
61, 2, 3, 5syl3an 1163 1 ((𝜑𝜃𝜂) → 𝜒)
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ∨ wo 836   ∧ w3a 1071 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8 This theorem depends on definitions:  df-bi 197  df-an 383  df-or 837  df-3an 1073 This theorem is referenced by:  suctrALT3  39682
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